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The impact of calibration models on the ability to detect and quantify analytes is substantial.

Nonetheless, use of the appropriate calibration models is poorly understood and poorly controlled, and in many cases we are instructed to use calibration models that produce false positives, false negatives, and wildly inaccurate quantitation.

The analyst may also employ a weighted least squares regression if replicate multi point curves have been performed 1/SD2

8000C

Weighting may significantly improve the ability of the regression to fit the linear model to the data.

The mathematics used in the least squares regression has a tendency to favor numbers of larger value over numbers of smaller value. Thus the regression curves that are generated will tend to fit points that are at the upper calibration levels better than those points at the lower calibration levels.

“An unweighted regression is incorrect for nearly all instruments and analytical systems.”

“The calibration included a data point at the Method 1631 MDL (0.2 ng/L). The RSD for the CF/WR approach was 7.8 percent. The coefficient of determination (r2) for the unweighted approach was 1.000, indicating no error in calibration. The reason for the indication of zero error is that the low calibration points are, essentially, unweighted. Therefore, the unweighted regression is equivalent to a single-point calibration at the highest calibration point. We do not believe that this form of calibration is consistent with the best science.”

“The correlation coefficient in the context of linearity testing is potentially misleading and should be avoided”

Royal Society of Chemistry, Technical brief

“The author has seen cases where a correlation coefficient of 0.997 was believed to be a better fit than 0.996 of a 5 point calibration curve. One can even find requirements in quality assurance plans to recalibrate if the correlation coefficient is less than 0.995!”

“Further, the Agency recognizes that the relative standard error (RSE) is a useful measure of the goodness of fit of a calibration model that the Agency had not previously considered. The RSE is useful for both linear regression models as well as non-linear models, as it considers the error at each point in the calibration model as a function of the concentration of that standard.”

“Using the RSE as a metric has the added advantage of allowing the same numerical standard to be applied to the calibration model, regardless of the form of the model. Thus, if a method states that the RSD should be <20% for the traditional linear model through the origin, then the RSE acceptance limit can remain 20% as well. Similarly, if a method provides an RSD acceptance limit of 15%, then that same figure can be used as the acceptance limit for the RSE.”